Tính E = 1/1.7 + 1/7.13 + 1/13.19 + + 1/31.37
Tính \(E = \frac{1}{{1.7}} + \frac{1}{{7.13}} + \frac{1}{{13.19}} + ... + \frac{1}{{31.37}}\).
\(E = \frac{1}{{1.7}} + \frac{1}{{7.13}} + \frac{1}{{13.19}} + ... + \frac{1}{{31.37}}\)
\(E = \frac{1}{6}\left( {\frac{6}{{1.7}} + \frac{6}{{7.13}} + \frac{6}{{13.19}} + ... + \frac{6}{{31.37}}} \right)\)
\(E = \frac{1}{6}\left( {1 - \frac{1}{7} + \frac{1}{7} - \frac{1}{{13}} + \frac{1}{{13}} - \frac{1}{{19}} + ... + \frac{1}{{31}} - \frac{1}{{37}}} \right)\)
\(E = \frac{1}{6}\left( {1 - \frac{1}{{37}}} \right) = \frac{1}{6}.\frac{{36}}{{37}} = \frac{6}{{37}}\)
Vậy \(E = \frac{6}{{37}}\).